Труды сотрудников ИВМ СО РАН

[Text] : статья / A. N. Gorban, M. Shahzad // Entropy. - 2011. - Vol. 13, Iss. 5. - p. 966-1019DOI 10.3390/e13050966 . -
Аннотация: We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events). This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.

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Shahzad, Muhammad; Горбань, Александр Николаевич

[Text] : статья / A. N. Gorban, G. S. Yablonskii // Chemical Engineering Science. - 2011. - Vol. 66, Iss. 21. - p. 5388-5399DOI 10.1016/j.ces.2011.07.054 . -
Аннотация: The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions, etc.), detailed mechanisms include both reversible and irreversible reactions. In this case, the principle of detailed balance cannot be applied directly. We represent irreversible reactions as limits of reversible steps and obtain the principle of detailed balance for complex mechanisms with some irreversible elementary processes. We prove two consequences of the detailed balance for these mechanisms: the structural condition and the algebraic condition that form together the extended form of detailed balance. The algebraic condition is the principle of detailed balance for the reversible part. The structural condition is the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reactions. Physically, this means that the irreversible reactions cannot be included in oriented cyclic pathways. The systems with the extended form of detailed balance are also the limits of the reversible systems with detailed balance when some of the equilibrium concentrations (or activities) tend to zero. Surprisingly, the structure of the limit reaction mechanism crucially depends on the relative speeds of this tendency to zero.

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Yablonskii, G.S.; Горбань, Александр Николаевич

[Text] : статья / G. S. Yablonsky [et al.] // EPL. - 2011. - Vol. 93, № 2. - Ст. 20004DOI 10.1209/0295-5075/93/20004 . -
Аннотация: We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, ẋ=Kx , the kinetic operator K is symmetric in the entropic inner product. This form of Onsager's reciprocal relations implies that the shift in time, exp(Kt), is also a symmetric operator. This generates the reciprocity relations between the kinetic curves. For example, for the Master equation, if we start the process from the i-th pure state and measure the probability pj(t) of the j-th state (j≠i), and, similarly, measure pi(t) for the process, which starts at the j-th pure state, then the ratio of these two probabilities pj(t)/pi(t) is constant in time and coincides with the ratio of the equilibrium probabilities. We study similar and more general reciprocal relations between the kinetic curves. The experimental evidence provided as an example is from the reversible water gas shift reaction over iron oxide catalyst. The experimental data are obtained using Temporal Analysis of Products (TAP) pulse-response studies. These offer excellent confirmation within the experimental error.

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Доп.точки доступа:
Yablonsky, G.S.; Gorban, A.N.; Горбань, Александр Николаевич; Constales, D.; Galvita, V.V.; Marin, G.B.